Average Error: 0.1 → 0.2
Time: 18.2s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{\sqrt{1 + \cos v \cdot e}} \cdot \frac{e}{\sqrt{1 + \cos v \cdot e}}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{\sqrt{1 + \cos v \cdot e}} \cdot \frac{e}{\sqrt{1 + \cos v \cdot e}}
double f(double e, double v) {
        double r475825 = e;
        double r475826 = v;
        double r475827 = sin(r475826);
        double r475828 = r475825 * r475827;
        double r475829 = 1.0;
        double r475830 = cos(r475826);
        double r475831 = r475825 * r475830;
        double r475832 = r475829 + r475831;
        double r475833 = r475828 / r475832;
        return r475833;
}
↓
double f(double e, double v) {
        double r475834 = v;
        double r475835 = sin(r475834);
        double r475836 = 1.0;
        double r475837 = cos(r475834);
        double r475838 = e;
        double r475839 = r475837 * r475838;
        double r475840 = r475836 + r475839;
        double r475841 = sqrt(r475840);
        double r475842 = r475835 / r475841;
        double r475843 = r475838 / r475841;
        double r475844 = r475842 * r475843;
        return r475844;
}

Error

Bits error versus e

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{\sqrt{1 + e \cdot \cos v} \cdot \sqrt{1 + e \cdot \cos v}}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{e}{\sqrt{1 + e \cdot \cos v}} \cdot \frac{\sin v}{\sqrt{1 + e \cdot \cos v}}}\]

  5. Final simplification0.2

    \[\leadsto \frac{\sin v}{\sqrt{1 + \cos v \cdot e}} \cdot \frac{e}{\sqrt{1 + \cos v \cdot e}}\]

Reproduce

herbie shell --seed 2019154 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))